Examples

f (x) = 4 x

$f (x) = 4 x$ ,

$g (x) = 3 x + 1$

Step 1

Find the difference of the functions.

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Step 1.1

Replace the function designators with the actual functions in

$f (x) - g x$ .

$4 x - (3 x + 1)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$4 x - (3 x) - 1 \cdot 1$

Step 1.2.2

Multiply

$3$ by

$- 1$ .

$4 x - 3 x - 1 \cdot 1$

Step 1.2.3

Multiply

$- 1$ by

$1$ .

$4 x - 3 x - 1$

Step 1.3

Subtract

$3 x$ from

$4 x$ .

$x - 1$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 3

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